Problem: Is ${422468}$ divisible by $4$ ?
Answer: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{4224} {68} = \gray{4224} \gray{00} + {68} $ Because $422400$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${68}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $68$ , divisible by $4$ Yes, ${68 \div 4 = 17}$, so $422468$ must also be divisible by $4$.